Lotteries are big business and a major revenue source for many governments. Acco
ID: 3183033 • Letter: L
Question
Lotteries are big business and a major revenue source for many governments. According to the North American Association of State and Provincial Lotteries, all but seven states in the United States have some type of lottery, and in 2010 these lotteries generated a national total of $78 billion in sales. About one-fourth of that money ($19 billion) ended up as state revenue, with the rest going to prizes and expenses.
1. Based on the data above and the U.S. population of approximately 315 million, how much does the average American spend on the lottery each year?
2. Surveys indicate that fewer than half of all Americans play the lottery in any given year. If half of all Americans play the lottery, what is the average spending per lottery player?
3. The table below gives recent prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery. Find the expected value of the winnings for a single lottery ticket, given the following grand prizes.
Prize
Probability
$10,000,000
1 in 175,223,510
$1,000,000
1 in 5,153,633
$10,000
1 in 648,976
$100
1 in 19,088
$100
1 in 12,245
$7
1 in 360
$7
1 in 706
$4
1 in 111
$4
1 in 55
$–1 (lose)
1 in 1
4. State how much you can expect to win or lose if you spend $365 per year on the lottery. Briefly discuss your results.v
Prize
Probability
$10,000,000
1 in 175,223,510
$1,000,000
1 in 5,153,633
$10,000
1 in 648,976
$100
1 in 19,088
$100
1 in 12,245
$7
1 in 360
$7
1 in 706
$4
1 in 111
$4
1 in 55
$–1 (lose)
1 in 1
Explanation / Answer
from above
hence expected value of the winnings for a single lottery ticket =$-0.60
4) total money lose if you spend $365 =365*0.60 = $-217.48
x P(X) xP(x) 10000000 0.00000 0.05707 1000000 0.00000 0.194038 1000 0.00000 0.001541 100 0.00005 0.005239 100 0.00008 0.008167 7 0.00278 0.019444 7 0.00142 0.009915 4 0.00901 0.036036 4 0.01818 0.072727 -1 1.00000 -1 -0.59582Related Questions
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